This story begins with Katie trying to solve the following problem:

In 36 years, my grandmother will be 100. How old is my grandmother now?

I am sure that it didn’t take you very long to solve this problem in your head. Now think of how you would approach this problem if you didn’t know or didn’t feel very comfortable with 2-digit arithmetic. Next, think about how long it would take you. Do you think paper and pencil would help?

I was trying to answer these questions for myself as I was waiting to see what Katie would do. She began by writing down numbers 1, 2, 3, … My initial thought was that she was going to write out all the numbers up to 100 and then cross out 36 starting from the end. I was wrong; her sequence stopped at 36. After a brief pause (during which I must admit I had no idea how she was going to proceed), she wrote 100 under the 36, 99 under the 35, 98 under the 34, and so on. Unfortunately, it was getting late and so I stopped her in the middle of this process and showed her the faster way of solving it, using double-digit addition. Now I will never know whether she would have stopped after writing 65 under the 1 or realized that she had to go down one more.

Throughout this whole activity, I twice found myself being pleasantly surprised. First, I didn’t expect her to attempt the problem without soliciting help. Second, I was pleased with the unique approach and that she decided to go through with it even though it was a lot of work. And of course I was upset with myself for not letting her finish. Did you ever have a situation when your kid came up with an interesting slow approach to a problem and you stopped them to show them a faster way? Did you regret it afterwards?

And here’s some more food for thought. When faced with a problem you have to solve, how often you ask yourself the following questions: Do I know how to solve this problem? Do I know of a fast way to solve it? If not, do I want to do it the slow way or spend time trying to come up with a faster method? This last one is usually the hard one for me – I find that I too often opt out for the slow (safe) way.

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About aofradkin

I enjoy thinking about presenting mathematical concepts to young children in exciting and engaging ways.

Your last paragraph shows that Katie follows your steps 🙂 Also the originality of her method completely compensates extra time spent. She is a good thinker.

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I agree that its great that she comes up with her own methods. I also agree that currently there’s no need to force the “quick” methods upon her – I’m sure she will come to them soon enough and perhaps with more understanding.

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This reminds me of my advisor. He likes to think about math problems while swimming. Sometimes he’ll figure out how to solve a problem, but then he’s still in the pool and has no paper and pencil to do the necessary calculations. So he tries to think of an easier solution so that he can do the computations in his head!

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This seems to be the opposite of what Katie is doing 🙂

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Parenting exhaustion means that I almost never stop their progress to show a faster way in anything. If they want to get dressed by testing every piece of clothing against every appendage, that just leaves me time to do my own math.

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Unfortunately, sometimes you’re working on a time-frame. I would love to give her all the time in the world to get dressed in the morning, but alas, then she’ll miss her schoolbus!

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